Deviations from Zipf's law contain more information than Zipf's law itself

Rank size plots of very different systems are usually fitted with Zipf's law, however, one often observes strong deviations at large sizes. We show that these deviations contain essential and general information on the evolution and the intrinsic cutoffs of the system. In particular, if the first ranks show deviations from Zipf's law, the empirical maximum represents the intrinsic upper cutoff of the physical system. Moreover, pure Zipf's law is always present whenever the underlying power-law size distribution is undersampled.